An electroagnetic wave is propagating along x-axis. At x = 1 m and t = 10 s, its electric vector `|vecE|=6V//m` then the magnitude of its magnetic vector is

Options

A. `2xx10^(-8)T`
B. `3xx10^(-7)T`
C. `6xx10^(-8)T`
D. `5xx10^(-7)T`

Answer

To find the magnitude of the magnetic vector \( |\vec{B}| \) of an electromagnetic wave given the electric vector \( |\vec{E}| \), we can use the relationship between the electric field and magnetic field in an electromagnetic wave. The relationship is given by:

\[ |\vec{B}| = \frac{|\vec{E}|}{c} \]

where \( c \) is the speed of light in vacuum, approximately \( 3 \times 10^8 \, \text{m/s} \).

### Step-by-Step Solution:

1. **Identify the given values:**
- Electric field magnitude \( |\vec{E}| = 6 \, \text{V/m} \)
- Speed of light \( c = 3 \times 10^8 \, \text{m/s} \)

2. **Use the formula to find the magnetic field:**
\[ |\vec{B}| = \frac{|\vec{E}|}{c} \]

3. **Substitute the values into the formula:**
\[ |\vec{B}| = \frac{6 \, \text{V/m}}{3 \times 10^8 \, \text{m/s}} \]

4. **Perform the division:**
\[ |\vec{B}| = \frac{6}{3 \times 10^8} = \frac{6}{3} \times 10^{-8} = 2 \times 10^{-8} \, \text{T} \]

5. **Conclusion:**
The magnitude of the magnetic vector \( |\vec{B}| \) is \( 2 \times 10^{-8} \, \text{T} \).

### Final Answer:
The magnitude of the magnetic vector is \( 2 \times 10^{-8} \, \text{T} \).

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